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Simplifying y2 + -7y + -4y = 7 + -28 Reorder the terms: -7y + -4y + y2 = 7 + -28 Combine like terms: -7y + -4y = -11y -11y + y2 = 7 + -28 Combine like terms: 7 + -28 = -21 -11y + y2 = -21 Solving -11y + y2 = -21 Solving for variable 'y'. Reorder the terms: 21 + -11y + y2 = -21 + 21 Combine like terms: -21 + 21 = 0 21 + -11y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -11y + -21 + y2 = 0 + -21 Reorder the terms: 21 + -21 + -11y + y2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -11y + y2 = 0 + -21 -11y + y2 = 0 + -21 Combine like terms: 0 + -21 = -21 -11y + y2 = -21 The y term is -11y. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11y + 30.25 + y2 = -21 + 30.25 Reorder the terms: 30.25 + -11y + y2 = -21 + 30.25 Combine like terms: -21 + 30.25 = 9.25 30.25 + -11y + y2 = 9.25 Factor a perfect square on the left side: (y + -5.5)(y + -5.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (y + -5.5) equal to 3.041381265 and -3.041381265.Subproblem 1
y + -5.5 = 3.041381265 Simplifying y + -5.5 = 3.041381265 Reorder the terms: -5.5 + y = 3.041381265 Solving -5.5 + y = 3.041381265 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = 3.041381265 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 3.041381265 + 5.5 y = 3.041381265 + 5.5 Combine like terms: 3.041381265 + 5.5 = 8.541381265 y = 8.541381265 Simplifying y = 8.541381265Subproblem 2
y + -5.5 = -3.041381265 Simplifying y + -5.5 = -3.041381265 Reorder the terms: -5.5 + y = -3.041381265 Solving -5.5 + y = -3.041381265 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = -3.041381265 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -3.041381265 + 5.5 y = -3.041381265 + 5.5 Combine like terms: -3.041381265 + 5.5 = 2.458618735 y = 2.458618735 Simplifying y = 2.458618735Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.541381265, 2.458618735}
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